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Proof step 200 from proof inv-evict (previous step)

# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files -- m), afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), key ∈ evict(m, pcache), m ∈ files, asynced1 → synced(files, icache, pcache), ∀ key. key ∈ pcache → key.data?, ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m ⊦ m = ROOT_INO, m ∈ dirs, key.data? ∧ # evict(m, pcache)[key].page = VFS_PAGE_SIZE ∧ key.ino ≠ m ∧ key.ino ∈ files ∧ (¬ evict(m, pcache)[key].dirty → key.part ∈ files[key.ino].content ∧ evict(m, pcache)[key].page = files[key.ino].content[key.part])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 201:
# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), evict(m, pcache)[key] = mkpentry(boolvar, buf), afs-cons(dirs, files), afs-cons(dirs, files -- m), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, key ∈ evict(m, pcache), asynced1 → synced(files, icache, pcache), ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m, ∀ key. key ∈ pcache → key.data? ⊦ m = ROOT_INO, m ∈ dirs, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ≠ m ∧ key.ino ∈ files ∧ (¬ boolvar → key.part ∈ files[key.ino].content ∧ buf = files[key.ino].content[key.part])

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [evict(m, pcache)[key], boolvar, buf]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: evict(m, pcache)[key], boolvar, buf